Related papers: Algebraic quantum field theory: objectives, method…
We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity…
We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees…
We construct a colored operad whose category of algebras is the category of algebraic quantum field theories. This is achieved by a construction that depends on the choice of a category, whose objects provide the operad colors, equipped…
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
I give a very brief introduction to the use of effective field theory techniques in quantum calculations of general relativity. The gravitational interaction is naturally organized as a quantum effective field theory and a certain class of…
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We…